Modular co-evolution of metabolic networks
© Zhao et al; licensee BioMed Central Ltd. 2007
Received: 08 March 2007
Accepted: 27 August 2007
Published: 27 August 2007
The architecture of biological networks has been reported to exhibit high level of modularity, and to some extent, topological modules of networks overlap with known functional modules. However, how the modular topology of the molecular network affects the evolution of its member proteins remains unclear.
In this work, the functional and evolutionary modularity of Homo sapiens (H. sapiens) metabolic network were investigated from a topological point of view. Network decomposition shows that the metabolic network is organized in a highly modular core-periphery way, in which the core modules are tightly linked together and perform basic metabolism functions, whereas the periphery modules only interact with few modules and accomplish relatively independent and specialized functions. Moreover, over half of the modules exhibit co-evolutionary feature and belong to specific evolutionary ages. Peripheral modules tend to evolve more cohesively and faster than core modules do.
The correlation between functional, evolutionary and topological modularity suggests that the evolutionary history and functional requirements of metabolic systems have been imprinted in the architecture of metabolic networks. Such systems level analysis could demonstrate how the evolution of genes may be placed in a genome-scale network context, giving a novel perspective on molecular evolution.
Cellular functions are carried out in a modular way, and functional modules are basic building blocks of cellular organization . From the perspective of molecular biology, a functional module is regarded as a group of spatially isolated or chemically specific biological components that work together for a discrete biological function. Various functional modules such as protein complexes [2–4], signalling/metabolic pathways [5–8] and transcriptional clusters [9, 10] have been detected from functional genomic techniques or bioinformatics analyses of genomic data. Recent studies suggest, to varying degrees, functional modules correlate with evolutionary modules , the latter being defined as cohesive evolutionary blocks in cellular systems [12, 13]. It was found that genes within functional modules tend to evolve in a coordinated way [12–15], while some fraction of evolutionary modules (or phylogenetic modules) agree well with known functional modules [16–19].
On the other hand, purely topological analysis by graph-theoretic methods has revealed that molecular networks, such as protein interaction [20–22], gene regulatory [23, 24] and metabolic networks [25–30], consist of topological modules – densely connected sub-networks within which there is a high density of edges, and between which there is a lower density of edges . Since graph-theoretic methods analyze networks from topological point of view using minimal prior knowledge about biological function or evolution, they have the potential to shed new light on biological systems based on the unbiased structural information . Actually, numerous studies have demonstrated, to some extent, topological modules in molecular networks tend to be functionally modularized [20–30]. Furthermore, studying molecular evolution from the viewpoint of network architecture is becoming a subject of current interest. Some recent studies suggested that the node degrees of molecular networks may constrain the evolution of proteins [33–38], and protein interaction hubs situated within modules are more evolutionarily constrained than those bridging different modules [39, 40]. However, little has been known about how network modularity affects protein evolution. Thus more studies are expected to reveal the possible correlation between topological modules and evolutionary modules in molecular networks.
In this study, we ask to which extent the identified topological modules of metabolic networks co-evolve. We explore this question by analysing the metabolic network of H. sapiens (hsa) reconstructed from the KEGG database [41–43]. We first break up the metabolic network into modules by the simulated annealing algorithm proposed in  and study the linkage pattern between modules. Then we investigate the evidence for co-evolution of modules by analysing the phylogenetic profiles, evolutionary ages and evolutionary rates of enzyme genes within modules. To mine the inherent relations between structure, function and evolution of metabolic networks, the features from H. sapiens network were then compared with those of the properly randomized counterparts, here, topological null model and biological null model, respectively.
Results and discussion
Identifying topological modules and their functions
We reconstructed the metabolic network of H. sapiens from the KEGG database [41–43] and represented the network by a directed substrate graph in such a way that the nodes correspond to metabolites and arcs correspond to enzyme-catalyzed reactions between these metabolites . The metabolic network of H. sapiens consists of 1378 metabolites and 666 enzymes, with the biggest connected cluster includes 948 metabolites and 614 enzymes.
Figure 1 exhibits a global view of interactions between modules, suggesting that the modules are linked in a core-periphery organized pattern [45, 46]. Some modules interact frequently and are interconnected densely to form a core, while others such as module 3, 6, 7 and 14 communicate with only one or two other modules and reside in the periphery of the network. We define the inter-module degree of one module as the number of its links with other modules, where a link by a bi-directed arc is counted as degree 2. Hence core modules have high inter-module degrees, while periphery modules have low inter-module degrees.
Inter-module degrees (d), number of nodes (N), and main functions of the topological modules for H. sapiens network
Function category and Main Function
Metabolism of essential human nutrients: Arachidonic acid metabolism
Metabolism of essential human nutrients: Phenylalanine, Tyrosine metabolism
Metabolism of essential human nutrients: Valine, leucine and isoleucine degradation, Propanoate metabolism
Metabolism of essential human nutrients: One carbon pool by folate
Metabolism of essential human nutrients: Nicotinate and nicotinamide metabolism
Hormonal compound biosynthesis and metabolism: Androgen and estrogen metabolism
Hormonal compound biosynthesis and metabolism: C21-Steroid hormone metabolism
Hormonal compound biosynthesis and metabolism: Biosynthesis of steroids
Hormonal compound biosynthesis and metabolism: Fatty acid biosynthesis
Glycan biosynthesis and metabolism: Blood group glycolipid biosynthesis – neo-lactoseries
Glycan biosynthesis and metabolism: N-Glycan biosynthesis; Fructose and mannose metabolism
Glycan biosynthesis and metabolism: Blood group glycolipid biosynthesis – neo-lactoseries; Ganglioside biosynthesis
Glycan biosynthesis and metabolism: Glycosphingolipid metabolism
Glycan biosynthesis and metabolism: Aminosugars metabolism
Metabolism of cofactor: Hemoglobin and urobilinogen biosynthesis
The similarity between the phylogenetic profiles of enzymes within modules
Average JC of the module is bigger than that of the global network.
The fraction of enzyme pairs with JC ≥ 0.66 (definition of a threshold) in the module is significantly bigger than 0.05, i.e., the fraction of that in the global network. We set the cutoff to 0.1.
The P-value is smaller than α = 0.05.
As shown in Figure 3, all modules except module 2 satisfy the criteria (1), in which 13 modules (module 7, 3, 25, 9, 16, 4, 6, 22, 12, 15, 19, 21 and 20) also satisfy the criteria (2). Of the 13 modules, only the P-value of module 20, which equals to 0.50067, is bigger than 0.05. That is to say, although the average JC of enzyme pairs in module 20 is big enough, and this module also includes a high fraction of enzymes with similar phylogenetic profiles, this case has a high probability to occur by chance. Thus module 20 could not be regarded as an evolutionary module by our criteria.
In summary, a total of 12 modules out of 25 (module 7, 3, 25, 9, 16, 4, 6, 22, 12, 15, 19 and 21) were found to be evolutionary modules, most of which are periphery modules. The inter-modules degree of eight modules are less than 5, suggesting that periphery modules behave more cohesively in evolution than core modules. That is to say, enzyme genes within periphery modules have higher tendency to be gained/lost together than those within core modules.
The evolutionary ages of modules
We classified enzyme genes in the H. sapiens network into seven evolutionary ages: Prokaryota, Protists, Fungi, Nematodes, Arthropods, Mammalian and Human. Hypergeometric cumulative distribution  was used to measure whether a module is more enriched with enzymes from a particular evolutionary age than would be expected by chance. Given significance level α = 0.05, a P-value smaller than α demonstrates low probability that the enzyme genes of a particular evolution age have appeared by chance.
More than 1/3 enzymes of this module belong to the evolutionary age;
The corresponding P-value is smaller than α = 0.05.
Evolutionary ages of topological modules for H. sapiens network
Percentage of enzymes in this age
9.26 × 10-8
2.46 × 10-4
6.19 × 10-3
3.02 × 10-4
1.58 × 10-6
2.22 × 10-3
4.18 × 10-2
2.34 × 10-3
1.89 × 10-2
6.82 × 10-3
4.27 × 10-5
3.5 × 10-6
2.53 × 10-2
6.48 × 10-4
2.65 × 10-2
1.61 × 10-3
The distribution feature of core and periphery modules in different evolutionary ages provides some evidence for the evolutionary history of metabolic networks. Matching the evolutionary ages of modules with their functions suggests how ancient cellular functions may have evolved to gain new phenotypes with improved adaptation: the core modules appeared earlier in evolution and communicate frequently to perform the basic functions, while the periphery modules "sprout" from the compactly inter-connected core modules later via sparse linkages to carry out some novel, specialized functions. In this way, the housekeeping functions are conserved in core modules while functional specialization is achieved by extending periphery modules.
Evolutionary rates of constituent enzyme genes of modules
We adopted the evolutionary rate to estimate the evolutionary constraints on metabolic enzymes. A small value of evolutionary rate suggests a smaller fraction of accepted amino acid substitutions (see Methods part), hence a higher evolutionary constraint on the enzyme. We extracted the evolutionary rate of each enzyme gene included in the H. sapiens metabolic network from the HomoloGene database , computed by the approaches in . Then the evolutionary rates were averaged over all enzyme genes within the same module.
Comparison of the H. sapiens network with its randomised counterparts
In order to investigate whether the topological, functional and evolutionary features of modularity we presented above are intrinsic for metabolic networks, we constructed two versions of randomised counterparts for the H. sapiens metabolic network and compared them with the real network.
We generated the second version of randomized network, called biological null model, through shuffling the enzymes that catalyze the reactions while preserving the network topology. At each step of randomization, we randomly chose two reactions that are catalyzed by different enzymes and then exchanged the enzymes catalyzing them. For one randomized network, we performed the same analysis about the functional distributions, phylogenic profiles, evolutionary ages, and evolutionary rates of its topological modules as we did for the H. sapiens network. Although the randomized network has the same topology as the H. sapiens network, its topological modules are high heterogeneity of reactions from different pathways [see Figure A1 of Additional file 1], thus could not be functional specific modules. From evolutionary view, enzymes within the same modules do not exhibit similar phylogenic profiles [see Figure A2 of Additional file 1]; neither the modules have specific evolutionary ages. In addition, the correlation between the average evolutionary rates of modules and the inter-module degrees is not statistically significant (Spearman's rank correlation between evolutionary rate and inter-module degrees was calculated as r = -0.0553, P-value = 0.793). These results demonstrate that the topological modules of the biological null model show absence of evolutionary modularity. Therefore, the functional and evolutionary modularity of topological modules could be inherent for metabolic networks.
In this study we have conducted a system-level survey about how evolution of enzyme genes is related to the structure and function of metabolic networks. From topological point of view, metabolic networks exhibit highly modular core-periphery organization pattern. Furthermore, the core modules are more evolutionarily conserved and perform some housekeeping metabolism functions, while the periphery modules appear later in evolution history and accomplish relatively specific functions. Our results suggest that the core-periphery modularity organization reflects the functional and evolutionary requirements of metabolic systems. The denser inter-connections between core modules may offer effectual protections to the basic metabolic process and keep the robustness of the metabolic system. On the other hand, the looser inter-linkages of periphery modules could function in favour of the flexibility and evolutionary ability of the system, so that the mutation or evolution of these parts may generate new phenotypes with improved adaptation while not significantly affecting other modules or even causing malfunction of the whole system. Our observation may shed light on a more global understanding of the topology, function and evolution for metabolic networks.
Data preparation and network reconstruction
In this study, the metabolic network of H. sapiens (hsa) was reconstructed using data downloaded (in May 2006) from the FTP service of KEGG (Kyoto Encyclopedia of Genes and Genomes). The "hsa_enzyme.list" file in the GENOME section of the KEGG database includes a list of the known enzymes encoded by H. sapiens's genome and the corresponding genes. The "reaction" file in the LIGAND section was first scanned for all reactions catalyzed by enzymes present in H. sapiens's genome, and totally 1492 reactions were determined. Then, the resulting reactions were matched to the "reaction_mapformula.lst" file, which includes direction information and the main metabolites for each reaction.
Some small molecules, such as adenosine triphosphate (ATP), adenosine diphosphate (ADP), nicotinamide adenine dinucleotide (NAD) and CO2, are normally used as carriers for transferring electrons or certain functional groups and participate in many reactions, while typically not participating in product formation. Therefore, in order to reflect biologically relevant transformations of substrates, we excluded these kinds of small molecules whose list is as follows [57, 58]:
ATP, ADP, AMP, NAD, NADH, NADP, NADPH, NH3, CoA, O2, CO2, Glu, Pyrophosphate, H+.
To construct the metabolic network, substrates and products were extracted from each of the enzyme-catalyzed reactions and all resulting substrate-product pairs were listed to specify the connections between the substances. A metabolic network is represented by a directed graph whose nodes correspond to metabolites and whose arcs correspond to reactions between these metabolites, in which irreversible reactions are presented as directed arcs while reversible ones as bi-directed arcs. For example, the irreversible reaction,
(S)-2-Methylmalate → Acetate + Pyruvate
corresponds to two directed arcs, i.e., (S)-2-Methylmalate → Acetate and (S)-2-Methylmalate → Pyruvate. The resulting metabolic network of H. sapiens embraces 1378 metabolites and 666 enzymes, in which 948 metabolites and 614 enzymes are included in the biggest connected cluster, while the other 52 enzymes and 430 metabolites scatter in 124 small clusters. Like previous studies of metabolic networks based on topology [25–30], we only analyze the biggest connected cluster.
Modularity and network decomposition
In this study, we applied the simulated annealing algorithm developed by Guimera and Amaral  to break up the metabolic network of H. sapiens into modules (The software Modul-w was kindly obtained from Guimera and Amaral). This algorithm identifies topological modules by maximizing the network's modularity metric through an exhaustive search, thus may generate the best decomposition of the network.
where r is the number of clusters, e ij is the fraction of arcs that leads between vertices of cluster i and j. The maximum modularity metric corresponds to the partition that comprises as many as within-module links and as few as possible inter-module links.
Hypergeometric distribution and P-value
Given significance level α, which is usually set as 0.05, a P-value smaller than α demonstrates low probability that the items with the desired feature are chosen by chance. Hence P-value can be used to measure whether the n samples drawn from the population is more enriched with items of the desired feature than would be expected by chance .
For every enzyme, its phylogenetic profile is defined as a binary vector that encodes its absence (0) or presence (1) in the reference genomes. In this study, we applied the method in [16, 17] to construct the phylogenetic profiles of enzymes. We first chose 115 organisms (16 eukaryote, 83 bacteria and 16 archaea) as reference genomes. To reduce the effect of bias in the organism distribution, we then merged these 115 genomes into 54 taxa according to the NCBI taxonomy [16, 17, 52] [see Table A1 in Additional file 1]. At last, the ENZYME section of the KEGG LIGAND database  was utilized to determine whether the corresponding enzyme is coded in the reference genomes or not. The resulting phylogenetic profile of each enzyme is a 54-dimention binary vector.
where n ij is the number of taxa that encode both enzyme i and j; n i , n j are the number of taxa that encode enzyme i and j, respectively.
Prokaryota: E. coli group [see Table A1 of Additional file 1]
Protists: Plasmodium falciparum, Trypanosoma brucei, Entamoeba histolytica
Fungi: Saccharomyces cerevisiae; Schizosaccharomyces pombe
Nematodes: Caenorhabditis elegans
Arthropods: Drosophila melanogaster
Mammalian: Mus musculus; Rattus norvegicus; Canis familiaris
Human: H. sapiens
An enzyme was assigned to evolutionary age of "Prokaryota" if an ortholog was detected in any organism of the 15th taxonomy in Table A1 of Additional file 1 (the E. coli group); "Protists" if an ortholog was detected in P. falciparum, or T. brucei, or E. histolytica but not in E. coli group; "Fungi" if an ortholog was detected in S. cerevisiae or S. pombe but not in E. coli group, P. falciparum, T. brucei, and E. histolytica, and so forth.
The evolutionary rate of an enzyme gene is defined as the normalized ratio of non-synonymous substitutions per nucleotide site (K a ) to synonymous substitutions per nucleotide site (K s ) that occurred in this enzyme gene . We extracted the evolutionary rate of every enzyme gene in the H. sapiens metabolic network based on the complete genome of Pan troglodytes from HomoloGene database . Nei and Gojobori's method  was used to calculate the synonymous and nonsynonymous substitution rates in HomoloGene database.
We thank Dr. Luís A. Nunes Amaral and Dr. Roger Guimerà for kindly providing us the software Modul-w for network decomposition; Dr. Jingchu Luo and Dr. Mikael Huss for suggestive comments on the manuscript; and the anonymous reviewers for their helpful comments. JZ thanks Dr. Petter Holme and Dr. Mikael Huss for stimulating discussions about modularity. This work was supported in part by grants from Ministry of Science and Technology China (2006AA02Z317, 2004CB720103, 2003CB715901, 2006AA02312), National High Technology Research and Development Program of China (2006AA020805), National Natural Science Foundation of China (30500107, 30670953, 30670574), International Cooperation Project of Science and Technology Commission of Shanghai Municipality (06RS07109), and Grant from Science and Technology Commission of Shanghai Municipality (04DZ19850, 06PJ14072, 04DZ14005).
- Hartwell LH, Hopfield JJ, Leibler S, Murray AW: From molecular to modular cell biology. Nature. 1999, 402: C47-C52. 10.1038/35011540.View ArticlePubMedGoogle Scholar
- Gavin AC, Bosche M, Krause R, Grandi P, Marzioch M, Bauer A, Schultz J, Rick JM, Michon AM, Cruciat CM: Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature. 2002, 415: 141-147. 10.1038/415141a.View ArticlePubMedGoogle Scholar
- Ho Y, Gruhler A, Heilbut A, Bader GD, Moore L, Adams SL, Millar A, Taylor P, Bennett K, Boutilier K: Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry. Nature. 2002, 415: 180-183. 10.1038/415180a.View ArticlePubMedGoogle Scholar
- Mewes HW, Frishman D, Guldener U, Mannhaupt G, Mayer K, Mokrejs M, Morgenstern B, Munsterkotter M, Rudd S, Weil B: MIPS: A database for genomes and protein sequences. Nucleic Acids Res. 2002, 30: 31-34. 10.1093/nar/30.1.31.PubMed CentralView ArticlePubMedGoogle Scholar
- Nakao M, Bono H, Kawashima S, Kamiya T, Sato K, Goto S, Kanehisa M: Genome-scale gene expression analysis and pathway reconstruction in KEGG. Genome Informatics. 1999, 10: 94-103.PubMedGoogle Scholar
- Kanehisa M, Goto S: KEGG: Kyoto Encyclopedia of Genes and Genomes. Nucleic Acids Res. 2000, 28 (1): 27-30. 10.1093/nar/28.1.27.PubMed CentralView ArticlePubMedGoogle Scholar
- Karp PD: Pathway databases: A case study in computational symbolic theories. Science. 2001, 293: 2040-2044. 10.1126/science.1064621.View ArticlePubMedGoogle Scholar
- Overbeek R, Larsen N, Pusch GD, D'Souza M, Jr ES, Kyrpides N, Fonstein M, Maltsev N, Selkov E: WIT: integrated system for high-throughput genome sequence analysis and metabolic reconstruction. Nucleic Acids Res. 2000, 28 (1): 123-125. 10.1093/nar/28.1.123.PubMed CentralView ArticlePubMedGoogle Scholar
- Salgado H, Santos-Zavaleta A, Gama-Castro S, Millan-Zarate D, Diaz-Peredo E, Sanchez-Solano F, Perez-Rueda E, Bonavides-Martinez C, Collado-Vides J: RegulonDB (version 3.2): Transcriptional regulation and operon organization in Escherichia coli K-12. Nucleic Acids Res. 2001, 29: 72-74. 10.1093/nar/29.1.72.PubMed CentralView ArticlePubMedGoogle Scholar
- van Nimwegen E, Zavolan M, Rajewsky N, Siggia ED: Probabilistic clustering of sequences: Inferring new bacterial regulons by comparative genomics. Proc Natl Acad Sci. 2002, 99: 7323-7328. 10.1073/pnas.112690399.PubMed CentralView ArticlePubMedGoogle Scholar
- Fraser HB: Coevolution, modularity and human disease. Current Opinion in Genetics & Development. 2006, 16: 637-644. 10.1016/j.gde.2006.09.001.View ArticleGoogle Scholar
- Snel B, Huynen MA: Quantifying modularity in the evolution of biomolecular systems. Genome Res. 2004 , 14: 391-397. 10.1101/gr.1969504.PubMed CentralView ArticlePubMedGoogle Scholar
- Campillos M, von Mering C, Jensen LJ, Bork P: Identification and analysis of evolutionarily cohesive functional modules in protein networks. Genome Res. 2006, 16: 374-382. 10.1101/gr.4336406.PubMed CentralView ArticlePubMedGoogle Scholar
- Chen Y, Dokholyan NV: The coordinated evolution of yeast proteins is constrained by functional modularity . Trends in Genetics. 2006, 22 (8): 416-419. 10.1016/j.tig.2006.06.008.View ArticlePubMedGoogle Scholar
- Pereira-Leal JB, Levy ED, Teichmann SA: The origins and evolution of functional modules:lessons from protein complexes. Phil Trans R Soc B. 2006, 361: 507-517. 10.1098/rstb.2005.1807.PubMed CentralView ArticlePubMedGoogle Scholar
- Yamada T, Kanehisa M, Goto S: Extraction of phylogenetic network modules from the metabolic network. BMC Bioinformatics. 2006, 7 (1): 130-10.1186/1471-2105-7-130.PubMed CentralView ArticlePubMedGoogle Scholar
- Yamada T, Goto S, Kanehisa M: Extraction of phylogenetic network modules from prokayrote metabolic pathways. Genome Informatics. 2004, 15: 249-258.PubMedGoogle Scholar
- von Mering C, Zdobnov EM, Tsoka S, Ciccarelli FD, Pereira-Leal JB, Ouzounis CA, Bork P: Genome evolution reveals biochemical networks and functional modules. Proc Natl Acad Sci. 2003, 100 (26): 15428-15433. 10.1073/pnas.2136809100.PubMed CentralView ArticlePubMedGoogle Scholar
- Spirin V, Gelfand MS, Mironov AA, Mirny LA: A metabolic network in the evolutionary context: Multiscale structure and modularity. Proc Natl Acad Sci. 2006, 103 (23): 8774-8779. 10.1073/pnas.0510258103.PubMed CentralView ArticlePubMedGoogle Scholar
- Spirin V, Mirny LA: Protein complexes and functional modules in molecular networks. Proc Natl Acad Sci. 2003, 100: 12 123-12 128. 10.1073/pnas.2032324100.View ArticleGoogle Scholar
- Rives AW, Galitski T: Modular organization of cellular networks. Proc Natl Acad Sci. 2003, 100: 1128-1133. 10.1073/pnas.0237338100.PubMed CentralView ArticlePubMedGoogle Scholar
- Gagneur J, Krause R, Bouwmeester T, Casari G: Modular decomposition of protein-protein interaction networks. Genome Biol. 2004, 5: R57-10.1186/gb-2004-5-8-r57.PubMed CentralView ArticlePubMedGoogle Scholar
- Ihmels J, Friedlander G, Bergmann S, Sarig O, Ziv Y, Barkai N: Revealing modular organization in the yeast transcriptional network. Nature Genetics. 2002, 31: 370 -3377.PubMedGoogle Scholar
- Ma HW, Buer J, Zeng AP: Hierarchical structure and modules in the Escherichia coli transcriptional regulatory network revealed by a new top-down approach. BMC Bioinformatics. 2004, 5: 199-10.1186/1471-2105-5-199.PubMed CentralView ArticlePubMedGoogle Scholar
- Ma HW, Zhao XM, Yuan YJ, Zeng AP: Decomposition of metabolic network into functional modules based on the global connectivity structure of reaction graph. Bioinformatics. 2004, 20 (12): 1870-1876. 10.1093/bioinformatics/bth167.View ArticlePubMedGoogle Scholar
- Gagneur J, Jackson DB, Casari G: Hierarchical analysis of dependency in metabolic networks. Bioinformatics. 2003, 19 (8): 1027-1034. 10.1093/bioinformatics/btg115.View ArticlePubMedGoogle Scholar
- Holme P, Huss M, Jeong H: Subnetwork hierarchies of biochemical pathways. Bioinformatics. 2003, 19 (4): 532-538. 10.1093/bioinformatics/btg033.View ArticlePubMedGoogle Scholar
- Guimera R, Amaral LAN: Functional cartography of complex metabolic networks. Nature. 2005, 433 (7028): 895-900. 10.1038/nature03288.PubMed CentralView ArticlePubMedGoogle Scholar
- Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabasi AL: Hierarchical Organization of Modularity in Metabolic Networks. Science. 2002, 297 (5586): 1551-1555. 10.1126/science.1073374.View ArticlePubMedGoogle Scholar
- Zhao J, Yu H, Luo J, Cao Z, Li Y: Hierarchical modularity of nested bow-ties in metabolic networks. BMC Bioinformatics. 2006, 7: 386-10.1186/1471-2105-7-386.PubMed CentralView ArticlePubMedGoogle Scholar
- Girvan M, Newman MEJ: Community structure in social and biological networks. Proc Natl Acad Sci. 2002, 99 (12): 7821-7826. 10.1073/pnas.122653799.PubMed CentralView ArticlePubMedGoogle Scholar
- Papin JA, Reed JL, Palsson BO: Hierarchical thinking in network biology: the unbiased modularization of biochemical networks. Trends in Biochemical Sciences. 2004, 29 (12): 641-647. 10.1016/j.tibs.2004.10.001.View ArticlePubMedGoogle Scholar
- Fraser HB, Hirsh AE, Steinmetz LM, Scharfe C, Feldman MW: Evolutionary Rate in the Protein Interaction Network. Science. 2002, 296: 750-752. 10.1126/science.1068696.View ArticlePubMedGoogle Scholar
- Wuchty S, Barabási AL, Ferdig MT: Stable evolutionary signal in a Yeast protein interaction network. BMC Evolutionary Biology. 2006, 6: 8-10.1186/1471-2148-6-8.PubMed CentralView ArticlePubMedGoogle Scholar
- Vitkup D, Kharchenko P, Wagner A: Influence of metabolic network structure and function on enzyme evolution. Genome Biology. 2006, 7 (5): R39-10.1186/gb-2006-7-5-r39.PubMed CentralView ArticlePubMedGoogle Scholar
- Light S, Kraulis P, Elofsson A: Preferential attachment in the evolution of metabolic networks. BMC Genomics. 2005, 6: 159-10.1186/1471-2105-6-159.PubMed CentralView ArticlePubMedGoogle Scholar
- Fraser H, Wall D, Hirsh A: A simple dependence between protein evolution rate and the number of protein-protein interactions. BMC Evolutionary Biology. 2003, 3 (1): 11-10.1186/1471-2148-3-11.PubMed CentralView ArticlePubMedGoogle Scholar
- Saeed R, Deane C: Protein protein interactions, evolutionary rate, abundance and age. BMC Bioinformatics. 2006, 7 (1): 128-10.1186/1471-2105-7-128.PubMed CentralView ArticlePubMedGoogle Scholar
- Fraser HB: Modularity and evolutionary constraint on proteins. Nature Genetics. 2005, 37 (4): 351-352. 10.1038/ng1530.View ArticlePubMedGoogle Scholar
- Ekman D, Light S, Bjorklund A, Elofsson A: What properties characterize the hub proteins of the protein-protein interaction network of Saccharomyces cerevisiae?. Genome Biology. 2006, 7 (6): R45-10.1186/gb-2006-7-6-r45.PubMed CentralView ArticlePubMedGoogle Scholar
- Goto S, Nishioka T, Kanehisa M: LIGAND: chemical database for enzyme reactions. Bioinformatics. 1998 , 14: 591-599. 10.1093/bioinformatics/14.7.591.View ArticlePubMedGoogle Scholar
- Goto S, Nishioka T, Kanehisa M: LIGAND: chemical database of enzyme reactions. Nucleic Acids Res. 2000, 28 (1): 380-382. 10.1093/nar/28.1.380.PubMed CentralView ArticlePubMedGoogle Scholar
- Goto S, Okuno Y, Hattori M, Nishioka T, Kanehisa M: LIGAND: database of chemical compounds and reactions in biological pathways. Nucleic Acids Res. 2002, 30 (1): 402-404. 10.1093/nar/30.1.402.PubMed CentralView ArticlePubMedGoogle Scholar
- Zhao J, Yu H, Luo J, Cao Z, Li Y: Complex networks theory for analyzing metabolic networks. Chinese Science Bulletin. 2006, 51 (13): 1529-1537. 10.1007/s11434-006-2015-2.View ArticleGoogle Scholar
- Borgatti SP, Everett MG: Models of core/periphery structures. Social Networks. 1999, 21: 375-395. 10.1016/S0378-8733(99)00019-2.View ArticleGoogle Scholar
- Holme P: Core-periphery organization of complex networks. Phys Rev E. 2005, 72: 46111-10.1103/PhysRevE.72.046111.View ArticleGoogle Scholar
- Tanaka T, Ikeo K, Gojobori T: Evolution of metabolic networks by gain and loss of enzymatic reaction in eukaryotes. Gene. 2006, 365: 88-94. 10.1016/j.gene.2005.09.030.View ArticlePubMedGoogle Scholar
- Csete M, Doyle J: Bow ties, metabolism and disease. Trends in Biotechnology. 2004, 22 (9): 446-450. 10.1016/j.tibtech.2004.07.007.View ArticlePubMedGoogle Scholar
- Dandekar T, Schuster S, Snel B, Huynen M, Bork P: Pathway alignment: application to the comparative analysis of glycolytic enzymes. Biochemical Journal. 1999, 343: 115-124. 10.1042/0264-6021:3430115.PubMed CentralView ArticlePubMedGoogle Scholar
- Huynen MA, Dandekar T, Bork P: Variation and evolution of the citric-acid cycle: a genomic perspective . Trends in Microbiology. 1999, 7 (7): 281-291. 10.1016/S0966-842X(99)01539-5.View ArticlePubMedGoogle Scholar
- Tavazoie S, Hughes JD, Campbell MJ, Cho RJ, Church GM: Systematic determination of genetic network architecture. Nat Genet. 1999, 22 (3): 281-285. 10.1038/10343.View ArticlePubMedGoogle Scholar
- Wheeler DL, Barrett T, Benson DA, Bryant SH, Canese K, Chetvernin V, Church DM, DiCuccio M, Edgar R, Federhen S, Geer LY, Helmberg W, Kapustin Y, Kenton DL, Khovayko O, Lipman DJ, Madden TL, Maglott DR, Ostell J, Pruitt KD, Schuler GD, Schriml LM, Sequeira E, Sherry ST, Sirotkin K, Souvorov A, Starchenko G, Suzek TO, Tatusov R, Tatusova TA, Wagner L, Yaschenko E: Database resources of the National Center for Biotechnology Information. Nucleic Acids Res. 2006, 34 (suppl_1): D173-180. 10.1093/nar/gkj158.PubMed CentralView ArticlePubMedGoogle Scholar
- Nei M, Gojobori T: Simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions. Mol Biol Evol. 1986, 3 (5): 418-426.PubMedGoogle Scholar
- Zhao J, Tao L, Yu H, Luo JH, Cao ZW, Li Y: Bow-tie topological features of metabolic networks and the functional significance. Chinese Science Bulletin. 2007, 52: 1036-1045. 10.1007/s11434-007-0143-y.View ArticleGoogle Scholar
- Maslov S, Sneppen K: Specificity and stability in topology of protein networks. Science. 2002, 296 (5569): 910-913. 10.1126/science.1065103.View ArticlePubMedGoogle Scholar
- Maslov S, Sneppen K, Zaliznyak A: Detection of topological patterns in complex networks: correlation profile of the internet. Physica A: Statistical and Theoretical Physics. 2004, 333: 529-540. 10.1016/j.physa.2003.06.002.View ArticleGoogle Scholar
- Ma H, Zeng AP: Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms. Bioinformatics. 2003, 19 (2): 270-277. 10.1093/bioinformatics/19.2.270.View ArticlePubMedGoogle Scholar
- Huss M, Holme P: Currency and commodity metabolites: Their identification and relation to the modularity of metabolic networks. IET Systems Biology. 2007, 1: 280-285. 10.1049/iet-syb:20060077.View ArticlePubMedGoogle Scholar
- Newman MEJ, Girvan M: Finding and evaluating community structure in networks. Physical Review E. 2004, 69: 26113-10.1103/PhysRevE.69.026113.View ArticleGoogle Scholar
- Lamboy WF: Computing genetic similarity coefficients from RAPD data: the effects of PCR artifacts. PCR Methods Appl. 1994, 4 (1): 31-37.View ArticlePubMedGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.